展开定理的补充和偶次B样条基函数

Supplement of Expansion Theorem and Even Order B-Spline Basis Function

在均匀分划的B样条展开定理中,奇次B样条以整数点展开,而对偶次B样条将如何展开,展开定理并未说明.通过时域的逼近计算,补充了偶次B样条在展开定理中的展开方式,提出了其基函数的一般构造方法.应用四次B样条基函数计算梁的弯曲,表明了偶次B样条展开方式的合理性,同时也表明了该基函数有较佳的逼近性能和适应性.研究成果属于逼近理论的基础部分,可以应用于需要逼近计算的诸多领域.

In the expansion theorem point, while even order B-spline has of uniformly-divided B-spline, odd order B-spline is expanded on integer not been demonstrated how to expand. By approximation computation of time domain, the supplement of the expansion form for even order B-spline is given in the expansion theorem. A generalized constructional method is put forward in basis function. By using quartic B-spline basis function to calculate the bending of a beam, the example proves the reasonability of the expansion form for even order B-spline, and shows that the even order B-spline basis function has good approximate property and adaptability. The results belong to the basic content of approximation theory and can be applied in various fields requiring approximation computation.